Problem: Simplify the following expression: $ n = \dfrac{1}{4} - \dfrac{-r - 3}{2r} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2r}{2r}$ $ \dfrac{1}{4} \times \dfrac{2r}{2r} = \dfrac{2r}{8r} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-r - 3}{2r} \times \dfrac{4}{4} = \dfrac{-4r - 12}{8r} $ Therefore $ n = \dfrac{2r}{8r} - \dfrac{-4r - 12}{8r} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{2r - (-4r - 12) }{8r} $ Distribute the negative sign: $n = \dfrac{2r + 4r + 12}{8r}$ $n = \dfrac{6r + 12}{8r}$ Simplify the expression by dividing the numerator and denominator by 2: $n = \dfrac{3r + 6}{4r}$